All printable ASCII characters can be entered directly. Those that are not alphanumeric are assigned explicit names in Mathematica, allowing them to be entered even on keyboards where they do not explicitly appear.

\[RawSpace]

!

\[RawExclamation]

"

\[RawDoubleQuote]

#

\[RawNumberSign]

$

\[RawDollar]

%

\[RawPercent]

&

\[RawAmpersand]

'

\[RawQuote]

(

\[RawLeftParenthesis]

)

\[RawRightParenthesis]

*

\[RawStar]

+

\[RawPlus]

,

\[RawComma]

-

\[RawDash]

.

\[RawDot]

/

\[RawSlash]

:

\[RawColon]

;

\[RawSemicolon]

<

\[RawLess]

=

\[RawEqual]

>

\[RawGreater]

?

\[RawQuestion]

@

\[RawAt]

[

\[RawLeftBracket]

\

\[RawBackslash]

]

\[RawRightBracket]

^

\[RawWedge]

_

\[RawUnderscore]

`

\[RawBackquote]

{

\[RawLeftBrace]

|

\[RawVerticalBar]

}

\[RawRightBrace]

~

\[RawTilde]

Full names for non-alphanumeric printable ASCII characters.

All characters which are entered into the Mathematica kernel are interpreted according to the setting for the CharacterEncoding option for the stream from which they came.

\[Name]

a character with the specified full name

\nnn

a character with octal code nnn

\.nn

a character with hexadecimal code nn

\:nnnn

a character with hexadecimal code nnnn

Ways to enter characters.

Codes for characters can be generated using ToCharacterCode. The Unicode standard is followed, with various extensions.

8-bit characters have codes less than 256; 16-bit characters have codes between 256 and 65535. Approximately 900 characters are assigned explicit names in Mathematica. Other characters must be entered using their character codes.

In general, what input syntax does is to determine how a particular string or collection of boxes should be interpreted as an expression. When boxes are set up, say with the notebook front end, there can be hidden InterpretationBox or TagBox objects which modify the interpretation of the boxes.

Character Strings

a character string

a literal in a character string

a literal in a character string

(at end of line)

ignore the following newline

a substring representing two-dimensional boxes

Entering character strings.

Character strings can contain any sequence of 8- or 16-bit characters. Characters entered by name or character code are stored the same as if they were entered directly.

In a notebook front end, text pasted into a string by default automatically has appropriate \ characters inserted so that the string stored in Mathematica reproduces the text that was pasted.

Within any box structures represented using backslash sequences can be used.

StringExpression objects can be used to represent strings that contain symbolic constructs, such as pattern elements.

Symbol Names and Contexts

name

symbol name

`name

symbol name in current context

context`name

symbol name in specified context

context`

context name

context1`context2`

compound context name

`context`

context relative to the current context

Symbol names and contexts.

Symbol names and contexts can contain any characters that are treated by Mathematica as letters or letter-like forms. They can contain digits but cannot start with them. Contexts must end in a backquote .

Numbers

digits

integer

digits.digits

approximate number

base^^digits

integer in specified base

base^^digits.digits

approximate number in specified base

mantissa*^n

scientific notation (mantissa×)

base^^mantissa*^n

scientific notation in specified base (mantissa×)

number`

machine-precision approximate number

number`s

arbitrary-precision number with precision

number``s

arbitrary-precision number with accuracy

Input forms for numbers.

Numbers can be entered with the notation in any base from to . The base itself is given in decimal. For bases larger than , additional digits are chosen from the letters - or -. Upper- and lower-case letters are equivalent for these purposes. Floating-point numbers can be specified by including in the digits sequence.

In scientific notation, mantissa can contain marks. The exponent must always be an integer, specified in decimal.

The precision or accuracy can be any real number; it does not need to be an integer.

In the form the precision is given in decimal, but it gives the effective number of digits of precision in the specified base, not in base 10.

An approximate number is taken to be machine precision if the number of digits given in it is Ceiling[$MachinePrecision]+1 or less. If more digits are given, then is taken to be an arbitrary-precision number. The accuracy of is taken to be the number of digits that appear to the right of the decimal point, while its precision is taken to be Log[10, Abs[x]]+Accuracy[x].

A number entered in the form 0``s is taken to have precision 0 and accuracy .

Bracketed Objects

Bracketed objects use explicit left and right delimiters to indicate their extent. They can appear anywhere within Mathematica input, and can be nested in any way.

The delimiters in bracketed objects are matchfix operators. But since these delimiters explicitly enclose all operands, no precedence need be assigned to such operators.

(*anytext*)

comment

(expr)

parenthesization: grouping of input

Bracketed objects without comma-separated elements.

Comments can be nested, and can continue for any number of lines. They can contain any 8- or 16-bit characters.

Parentheses must enclose a single complete expression; neither nor are allowed.

There is no issue of precedence for forms such as and in which operands are effectively spanned by the operator. For forms such as and a left precedence does need to be specified, so such forms are included in the main table of precedences above.

Input of Boxes

• Use a palette

• Use control keys

Ways to input boxes.

Control Keys

Ctrl+2 or Ctrl+@

square root

Ctrl+5 or Ctrl+%

switch to alternate position (e.g. subscript to superscript)

Ctrl+6 or Ctrl+^

superscript

Ctrl+7 or Ctrl+&

overscript

Ctrl+9 or Ctrl+(

begin a new cell within an existing cell

Ctrl+0 or Ctrl+)

end a new cell within an existing cell

Ctrl+- or Ctrl+_

subscript

Ctrl+4 or Ctrl+$

underscript

Ctrl+Enter

create a new row in a table

Ctrl+,

create a new column in a table

Ctrl+.

expand current selection

Ctrl+/

fraction

Ctrl+Space

return from current position or state

Ctrl+, Ctrl+, Ctrl+, Ctrl+

move an object by minimal increments on the screen

Standard control keys.

On English-language keyboards both forms will work where alternates are given. On other keyboards the first form should work but the second may not.

Boxes Constructed from Text

When textual input that you give is used to construct boxes, as in StandardForm or TraditionalForm cells in a notebook, the input is handled slightly differently from when it is fed directly to the kernel.

The input is broken into tokens, and then each token is included in the box structure as a separate character string. Thus, for example, is broken into the tokens , , .

• symbol name (e.g. )

• number (e.g. )

• operator (e.g. )

• spacing (e.g. )

• character string (e.g. )

Types of tokens in text used to construct boxes.

A RowBox is constructed to hold each operator and its operands. The nesting of RowBox objects is determined by the precedence of the operators in standard Mathematica syntax.

Note that spacing characters are not automatically discarded. Instead, each sequence of consecutive such characters is made into a separate token.

String-Based Input

\(...\)

input raw boxes

\!\(...\)

input and interpret boxes

Inputting raw and interpreted boxes.

Any textual input that you give between and is taken to specify boxes to construct. The boxes are only interpreted if you specify with that this should be done. Otherwise is left for example as SuperscriptBox, and is not converted to Power.

Within the outermost , further specify grouping and lead to the insertion of RowBox objects.

When you input typesetting forms into a string, the internal representation of the string uses the above forms. The front end displays the typeset form, but uses the notation when saving the content to a file or when sending the string to the kernel for evaluation.

The Extent of Input Expressions

Mathematica will treat all input that you give on a single line as being part of the same expression.

Mathematica allows a single expression to continue for several lines. In general, it treats the input that you give on successive lines as belonging to the same expression whenever no complete expression would be formed without doing this.

Thus, for example, if one line ends with , then Mathematica will assume that the expression must continue on the next line. It will do the same if for example parentheses or other matchfix operators remain open at the end of the line.

If at the end of a particular line the input you have given so far corresponds to a complete expression, then Mathematica will normally begin immediately to process that expression.

You can however explicitly tell Mathematica that a particular expression is incomplete by putting a or a (\[Continuation]) at the end of the line. Mathematica will then include the next line in the same expression, discarding any spaces or tabs that occur at the beginning of that line.

Special Input

?symbol

get information

??symbol

get more information

?s1s2...

get information on several objects

!command

execute an external command (text-based interface only)

!!file

display the contents of an external file (text-based interface only)

Special input lines.

In most implementations of Mathematica, you can give a line of special input anywhere in your input. The only constraint is that the special input must start at the beginning of a line.

Some implementations of Mathematica may not allow you to execute external commands using !command.

Front End Files

Notebook files as well as front end initialization files can contain a subset of standard Mathematica language syntax. This syntax includes: